TASK: Based on what you know about multiplying exponents, make a prediction about what you think the rule is for dividing exponents. Why do you think this is the rule?
Look at the following examples:
Example 1:
Example 2:
Example 3:
TASK: Does your prediction seem to be true? If not, based on the three examples given, what do you think the rule for dividing exponents is?
When we divide exponents we have to do two things:
1. Divide the coefficients (if they don't divide evenly, we can reduce the fraction - like Example 3)
2. Divide the powers with the same base by keeping the same base and subtracting the exponents (numerator - denominator).
What do we do if we subtract the exponents and get a negative number?
If the exponent is negative when we subtract, that means that the power will be in the denominator of the fraction.
Example:
In this example, when we subtract the exponents with the "x"s, we get 2-5 = -3. This tells us that the x to the third power is going to be in the denominator (and the exponent becomes positive). The same thing happens with the "y"s. 8-10 = -2, so y to the second power is in the denominator. When we subtract the "z"s, the difference is positive 1, so the remaining "z" stays in the numerator.
What do we do if there is no other power with the same base?
If there is no other power with the same base, we just bring the base and the exponent down into the answer on it's own.
Example:
In this example, we could divide the coefficients and we could subtract the exponents with the "q" and the "r." However, the "s" and the "t" did not have another power to divide with, so we can just carry them over as they are into the answer.
TASK: Open the document below and answer each of the Regents questions. Turn your work in during class.
Look at the following examples:
Example 1:
Example 2:
Example 3:
TASK: Does your prediction seem to be true? If not, based on the three examples given, what do you think the rule for dividing exponents is?
When we divide exponents we have to do two things:
1. Divide the coefficients (if they don't divide evenly, we can reduce the fraction - like Example 3)
2. Divide the powers with the same base by keeping the same base and subtracting the exponents (numerator - denominator).
What do we do if we subtract the exponents and get a negative number?
If the exponent is negative when we subtract, that means that the power will be in the denominator of the fraction.
Example:
In this example, when we subtract the exponents with the "x"s, we get 2-5 = -3. This tells us that the x to the third power is going to be in the denominator (and the exponent becomes positive). The same thing happens with the "y"s. 8-10 = -2, so y to the second power is in the denominator. When we subtract the "z"s, the difference is positive 1, so the remaining "z" stays in the numerator.
What do we do if there is no other power with the same base?
If there is no other power with the same base, we just bring the base and the exponent down into the answer on it's own.
Example:
In this example, we could divide the coefficients and we could subtract the exponents with the "q" and the "r." However, the "s" and the "t" did not have another power to divide with, so we can just carry them over as they are into the answer.
TASK: Open the document below and answer each of the Regents questions. Turn your work in during class.